Hi everyone, I have trouble depicting the difference between these two problems. The first problem uses the multiplication rule to solve while the second problem uses the counting rules (combination) to solve. To me, it seems like both problems could be solved using the multiplication rule so I don't understand why the second problem is solved using combination...

If I reword the second problem, I could reword it as the following:

Wouldn't this make it the exact same as problem #1, meaning I could solve #2 the same way I solved #1?

If you do it right. Remember there is one free card which can be anything. In addition as you draw the five cards in sequence, the free card may be in any position, so you have to add up five cases (actually multiply one case by 5, since the probabilities are all the same).